Optimal buffer inventory and preventive maintenance for an imperfect production process

In this paper we present a model to determine the optimal length of continuous production periods between maintenance actions and the optimal buffer inventory to satisfy demand during preventive maintenance or repair of a manufacturing facility. We include in the model the possibility of imperfect production. We consider that the duration and cost of the maintenance action depend on the state of the production facility.     

Optimal order release dates for two-level assembly systems with stochastic lead times at each level

In this paper, we examine an optimisation problem for component replenishment in two-level assembly systems under stochastic lead times. The Assembly-to-Order principle is applied. The demand for a finished product and its planned due date are known. The capacity of the assembly system at each level is considered infinite. At each level, the assembly process starts when all the required components or semi-finished items are available. At the second level, the components are ordered from external suppliers and order release dates are decision variables of the problem. A backlogging cost is incurred if the finished product demand is satisfied after the planned due date. If the finished product, a given component or a semi-finished product is available before the corresponding assembly date, an inventory holding cost is considered. Genetic algorithms (GA) reinforced with different techniques are developed to find order release dates that minimise the total expected cost. A Branch and Bound method is also developed to assess the effectiveness of the hybrid GA. Regardless of the number of components and the variability of the costs related to the finished product, the experimental results indicate that the proposed GA are highly efficient.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

Joint optimisation of maintenance and production policies considering random demand and variable production rate

This paper deals with a randomly failing manufacturing system M1 which has to satisfy a random demand during a finite horizon given a required service level. To help meet this demand, subcontracting is used through another production system M2. M1 operates with a variable production rate and its failure rate depends on both time and the production rate. In these conditions, as a first step, we establish a preliminary production plan corresponding to a given service level. In a second stage, we integrate the effect of the machine degradation introducing a unitary degradation cost. The optimal production plan is then obtained by minimising the sum of the production, the inventory and the degradation costs. In the final stage, we propose another optimal plan combined with a preventive maintenance policy aiming at reducing the machine degradation while minimising the total cost including the production, inventory and maintenance costs.     

The use of rush deliveries in periodic review assemble-to-order systems

We calculate optimal safety stock in a periodic review (T,S) assemble-to-order system having multiple components and multiple finished goods (FGs). Customer orders for FGs arrive according to independent Poisson processes, and cannot be neither backlogged nor lost. In case of potential component stock-out, the studied system uses rush deliveries from suppliers. For this setting, approximate expressions of the optimal safety stock that minimise the sum of inventory holding and rush ordering costs are developed. Exact optimal safety stocks are calculated using Discrete Event Simulation, and compared numerically to the approximate expressions. The model is applied to a first-tier automotive supplier and yields to a significant reduction in terms of inventory holding and rush ordering costs. A sensitivity analysis on relevant system parameters such as components demand, assembly coefficients and unit rush ordering cost is conducted.     

Forecasting and maintenance problem under subcontracting constraint with transportation delay

In this paper, a forecasting production/maintenance optimization problem has been proposed with a random demand and single machine M₁ on a finite horizon. The function rate of the machine M₁ is depending on the production rate for each period of the forecasting horizon. In order to satisfy the customer, a subcontracting assures the rest of the production through machine M₂ with transportation delay. An analytic formulation of the problem has been proposed using a sequential computation of the optimal production plan for which an optimal preventive maintenance policy has been calculated based on minimal repair. Firstly, we find, the optimal production plans of principal and subcontracting machines, which minimises the total production and inventory cost for the cases without and with returned products under service level and subcontracting transportation delay. Secondly, we determine a joint effective maintenance policy with the optimal production plan, which integrates the various constraints for the production rates, the transportation delay and the returned production deadline. Numerical results are presented to highlight the application of the developed approach and sensitivity analysis shows the robustness of the model.     

Preventive maintenance and replacement policies for deteriorating production systems subject to imperfect repairs

This paper presents a special case of integration of the preventive maintenance into the repair/replacement policy of a failure-prone system. The machine of the considered system exhibits increasing failure intensity and increasing repair times. To reduce the failure rate and subsequent repair times following a failure, there is an incentive to perform preventive maintenance on the machine before failure. When a failure occurs, the machine can be repaired or replaced by a new one. Thus the machine's mode at any time can be classified as either operating, in repair, in replacement or in preventive maintenance. The decision variables of the system are the repair/replacement switching age or number of failures at the time of the machine's failure and the preventive maintenance rate. The problem of determining the repair/replacement and preventive maintenance policies is formulated as a semi-Markov decision process and numerical methods are given in order to compute optimal policies which minimise the average cost incurred by preventive maintenance, repair and replacement over an infinite planning horizon. As expected, the decisions to repair or to replace the machine upon a failure are modified by performing preventive maintenance. A numerical example is given and a sensitivity analysis is performed to illustrate the proposed approach and to show the impact of various parameters on the control policies thus obtained.     

Manufacturing lot-sizing,procurement and delivery schedules over a finite planning horizon

In this study, an integrated manufacturing system for technology-related companies whose products are experiencing continuous price decrease during the life cycle is studied for optimal procurement, production and delivery schedules over a finite planning horizon. The model considers the inventory cost both at manufacturing and at delivery from supplier. Since the price is continuously decreasing, a manufacturing firm delivers the finished goods in small quantities frequently. Frequent deliveries in small lots are effective to reduce the total cost of the supply chain. The key for high-tech industries is to reduce the inventory holding time since the component prices are continuously decreasing, and this can only be achieved by implementing an efficient supply chain. Therefore, the main purpose of this paper is to develop an integrated inventory model for high-tech industries in JIT environment under continuous price decrease over finite planning horizon while effectively and successfully accomplishing supply chain integration so that the total cost of the system is minimal. An efficient algorithm is developed to determine the optimal or near-optimal lot sizes for raw material procurement, and manufacturing batch under a finite planning horizon. Finally, the solution technique developed for the model is illustrated with numerical examples.     

Optimal maintenance schedule decisions for machine tools considering the user's cost structure

This paper proposes a model for obtaining optimal preventive repair and replacement intervals of a machine tool subassembly considering the user's cost structure and the effect of major overhauls. Corrective actions are considered as minimal, whereas preventive repair and major overhauls are considered as imperfect in this paper. The objective is to obtain optimal repair/replacement decisions for the machine tool subassembly such that the expected life-cycle cost contribution over the whole life of the system is minimised. The proposed strategy improves over other existing strategies since it simultaneously considers the effects of the user's cost structure and major overhauls, while optimising the preventive repair and replacement intervals. A numerical illustration is provided to demonstrate the general application of the proposed approach.     

Production and maintenance integrated planning

This paper introduces an expert system for the planning and management of a multi-product and one-stage production system made up of flexible machines operating in parallel. The following characteristics of the production system were considered: production costs depending on the machine and on the job processed, setups depending on the machine and on the job-processing sequence, preventive maintenance, order portfolio defined by order quantities, release dates and due dates.

The system schedules both production and maintenance at the same time. It pursues three objectives: to meet release and due dates, to minimize the total cost of the plan (sum of the expected maintenance cost, the setup cost and the production cost) and to minimize the total plant utilization time (sum of the total job processing time, the total setup time, the total machine idle time and the total maintenance time).     

A variable neighbourhood search for integrated production and preventive maintenance planning in multi-state systems

This paper presents a variable neighbourhood search (VNS) to the integrated production and maintenance planning problem in multi-state systems. VNS is one of the most recent meta-heuristics used for problem solving in which a systematic change of neighbourhood within a local search is carried out. In the studied problem, production and maintenance decisions are co-ordinated, so that the total expected cost is minimised. We are given a set of products that must be produced in lots on a multi-state production system during a specified finite planning horizon. Planned preventive maintenance and unplanned corrective maintenance can be performed on each component of the multi-state system. The maintenance policy suggests cyclical preventive replacements of components, and a minimal repair on failed components. The objective is to determine an integrated lot-sizing and preventive maintenance strategy of the system that will minimise the sum of preventive and corrective maintenance costs, setup costs, holding costs, backorder costs and production costs, while satisfying the demand for all products over the entire horizon. We model the production system as a multi-state system with binary-state components. The formulated problem can be solved by comparing the results of several multi-product capacitated lot-sizing problems. The proposed VNS deals with the preventive maintenance selection task. Results on test instances show that the VNS method provides a competitive solution quality at economically computational expense in comparison with genetic algorithms.     

A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system

Re-manufacturing is recycling by manufacturing as-good-as-new products from used products, often involving disassembly, cleaning, testing, part replacement/repair, and re-assembly operations. Production planning and inventory control is one of the most important research issues for re-manufacturing system, which are faced with a greater degree of uncertainty and complexity. This leads to a critical need for planning and control systems designed to deal with the added uncertainty and complexity. We formulate a stochastic dynamic programming based model to study the production planning, i.e. dynamic lot sizing problem, of re-manufacturing systems. In the model the demand and return amounts are stochastic over the finite planning horizon. The objective is to determine the quantities that have to be re-manufactured at each period in order to minimise the total cost, including re-manufacturing cost, holding cost for returns and re-manufactured products and backlog cost. The optimal production plan of the re-manufacturing system over a finite planning horizon can be obtained with the policy iteration method. In the end, a numerical example is performed to illustrate how the model is applied and to prove its feasibility.     

Generalized newsboy model to compute the optimal planned lead times in assembly systems

Assembly systems with one type of finished product and several types of components are studied. The lead times of components are random variables, and the finished product demand is constant. The criterion considered is the sum of the average holding cost for the components and the average backlogging cost for the finished product. The decision variables are the planned lead times of components. A model that gives the optimal values for the planned lead times is proposed. From a practical point of view, this model can be used to calculate the safety lead time on assembly systems under supply uncertainty, and from a theoretical point of view, it is a generalization of the well-known discrete newsboy model.     

考虑预防维修时间及相关性的多部件系统维护策略

针对动车组关键系统维修过程中涉及部件数量多、维修时间长、维修费用高的特点，提出了预防维修时间、故障相关性、经济相关性3重因素影响下的多部件系统机会维护策略。首先对多部件建立部件故障率模型。在此基础上，考虑预防维修时间，将部件层预防维修成本分为独立时间成本和依赖时间成本，对经济相关性进行建模，再以系统维修费用率最小为优化目标建立系统层维护模型，并应用遗传算法求解。最后通过算例表明，相较于考虑单一因素的维修策略，所提维修策略可降低系统维修成本10%及以上，验证了考虑维修时间和部件联合相关性的必要性和有效性。     

Flow control of two-level assembly lines

The paper addresses the flow control problem in two-level assembly production lines composed of a unique assembly machine and multiple upper level machines. In order to obtain a finished product, the assembly machine needs components produced by different upper level machines. We assume that the production capacity of each machine is constant and the demand is known over the whole problem horizon. Backlogging is not allowed. The flow control problem consists of adjusting the production of the machines in order to minimize the total cost incurred by holding components and finished products. Properties of the optima) solutions are given. Based on these properties, we propose a simple analytical solution.     

Optimal integrated maintenance/production policy for randomly failing systems with variable failure rate

This article deals with the combined production and maintenance plans for a manufacturing system satisfying a random demand. We first establish an optimal production plan which minimises the average total inventory and production cost. Second, using this optimal production plan, and taking into account the deterioration of the machine according to its production rate, we derive an optimal maintenance schedule which minimises the maintenance cost. A numerical example illustrates the proposed approach, this analytical approach, based on a stochastic optimisation model and using the operational age concept, reveals the significant influence of the production rate on the deterioration of the manufacturing system and consequently on the integrated production/maintenance policy.     

Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.     

FPA method for optimal production planning under availability/degradation machine and subcontracting constraint

This work treats an industrial problematic of a manufacturing system M₁ subject to random failure and that satisfies a random demand under required service level. To ensure the satisfaction of the demand, it calls up on a second manufacturing system M₂ that is a subcontractor and has a stochastic service level. This paper aims to determine an optimal production plan taking into account the degradation of the manufacturing system following its production rate and its availability. The unavailability of the machine M₁ is due to the non-negligible preventive and corrective maintenance actions duration. To consider a realistic case of the subcontractor, we consider that is not able to respond to the variation of the demand, and then it assumed that the manufacturer can order a minimum fixed quantity. We then derive an optimal production plan taking into account the degradation of the machine and simultaneously minimising: inventory, degradation and production cost. An algorithm based on finite perturbation analysis is proposed to determine the optimal production plan and the sensitivity study of the availability is presented.     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.